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Differential Supply Systems

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IV.II.1 Differential supply systems

Under perfect competition the firm's marginal cost (with respect to input z) equals the price y of the output good (which is exogenously given since the firm is a price taker). Formally this implies

Differential Supply Systems

(IV.II.1-1)

Suppose the firm sells m products z at prices y then total revenue (TR) can be written as

(IV.II.1-2)

Furthermore, the share of revenue of product i and Divisia's volume index can be defined as

(IV.II.1-3)

respectively.

Since the firm operates under perfect competition and profit maximization (c.q. marginal returns equal marginal costs) it follows that for each product (IV.II.1-1) can be applied

(IV.II.1-4)

A differential output supply system can be proved to be described by

(IV.II.1-5)

where

(IV.II.1-6)

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